标题： 纽结不变量和不定因果顺序 显示英文标题

标题： Knot invariants and indefinite causal order

摘要： 我们探讨在叠加的准经典时空背景下事件之间的不确定因果顺序。 我们引入了几种新的量化指标来衡量任意有限数量事件和叠加时空配置中因果顺序的不确定程度。 通过构建事件之间因果顺序的图示和纽结理论表示，我们发现因果顺序的确定性或最大不确定性的性质是拓扑不变的。 这揭示了量子因果关系领域与纽结理论之间的有趣联系。 此外，我们提供了一种不确定因果顺序的操作编码，并讨论了如何将量子相干性的度量纳入我们的分类中。 显示英文摘要

摘要： We explore indefinite causal order between events in the context of quasiclassical spacetimes in superposition. We introduce several new quantifiers to measure the degree of indefiniteness of the causal order for an arbitrary finite number of events and spacetime configurations in superposition. By constructing diagrammatic and knot-theoretic representations of the causal order between events, we find that the definiteness or maximal indefiniteness of the causal order is topologically invariant. This reveals an intriguing connection between the field of quantum causality and knot theory. Furthermore, we provide an operational encoding of indefinite causal order and discuss how to incorporate a measure of quantum coherence into our classification.